Activities in the classroom

72

5.3 Activities in the classroom

The arrangement of learning space has a significant impact on operatives that can be provided for teaching and leaning. The following are some arrangements of computer-based technologies.  Fully integrated classroom promote maxim use of computer at times when they are needed by individualsor group of students  Special computer rooms or computer laboratories give students access to computers within a set time frame.  Computer based resources are rapidly replacing print-based materials i.e. Internet is used as a library. The process of up-taking the computer-based technology in education involves five stages: the first stage involves the process of learning the new skills about how to use a computer and its applications. The second stage is how to make the exact copy or replicate the established practical, that is, adoption. The third stage involves the process of learners to use or integrate the technology acquired into their own practice. The fourth stage is the process of using that technology in cooperative and multidisciplinary work, and the last stage involves the process of devising new uses of the technology as a tool for teaching and learning. Learning mathematical ideas is difficult for students. Teacher often struggles to find ways to help their students understand very abstract notions. As a teacher face this challenges heshe must think about how best to help the studentslearners form understanding of mathematical abstractions. The job of the teacher is to help learners to construct internal representations i.e. cognitive abstraction of mathematical concepts that are developed through experience embodied in external representations i.e. physical objects, such as graphs, tables, diagrams, and charts.

5.3.1 Presenting the concept of a quadratic equation

. Let` s examine the concept of a quadratic equation prefer square as an example. In the power -current curve the steepness of the curve is an 73 indication of how power increases or decrease depending in the current supplied to the system. This study focuses on the relationship between the current flowing into the system and the power given out by that system. The internal representation is how the change in current affects the power and the external representation is the curve showing the relationship between the current and power. The relationship between the power and the current is represented in a quadratic equation y = x 2 – 6x + 9, in which the initial conditions are stated, such that at a certain value of current e.g. when the current is 3 amperes the power given out becomes zero. The chart below shows the relationship between the current and power. Current in Amps Power in Watts 1 4 2 1 3 4 1 5 4 6 9 7 16 8 25 9 36 10 49 11 64 12 81 13 100 Table 1. The relationship between current and power The teacher must grapple with how to help students understand the concept of the rate of change of one quantity current in relation to another power. 74 Power and Current Relationship 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 Current in Amps P o w er in W at ts Power in Watts Graph 1. The relationship between the current and power That is, the teacher must help students form accurate internal representation of an abstract mathematical concept embodied in the graph. Representations have been classified in many ways. For example, Bruner 1996, as cited in Janvier, Girardon and Morand, 1993 developed one important approach. In this scheme, representations are categorized as enactive, iconic or symbolic. Enactive representations refer to the activity basis of a concept e. g. how the change in current affects the power Iconic representations refer to the images that embody the concept e. g the curve, and symbolic representations refer to the characters that mathematicians have agreed upon to represent the mathematical concept e.g. the quadratic equation that relates the power and current. From the table and graph shown above the main concept is that, there is only a single value of current for which the power is zero and the general knowledge is that, quadratic equations must have two solution, it means that, such quadratic equations have repeated roots, which is a definition of perfect squares. 75

5.3.2 Using Technology to Enhance Experience

. How might the teacher provide this experience? One suggestion is through the use of technology. For example, in this study the spreadsheet which is formatted with formulas in some fields to solve quadratic equations of the form y = ax 2 + bx + c where a  0 and then to verify the relation b 2 = 4ac is used to help students form an understanding of the concept of quadratic equations prefect squares. Where y represents power and x represents current. The table below shows a spreadsheet, which formatted with formulas to help students in learning. 1 st solution 2 nd solution Perfect Square? b 2 = 4ac? =-B2+SQRTB2B2-4A2C22A2 =-B2-SQRTB2B2-4A2C22A2 =IFD2=E2, yes”,” no =IFB2B2=4A2C2, yes”,” no =-B3+SQRTB3B3-4A3C32A3 =-B3-SQRTB3B3-4A3C32A3 =IFD3=E3, yes”,” no =IFB3B3=4A3C3, yes”,” no =-B4+SQRTB4B4-4A4C42A4 =-B4-SQRTB4B4-4A4C42A4 =IFD4=E4, yes”,” no =IFB4B4=4A4C4, yes”,” no =-B5+SQRTB5B5-4A5C52A5 =-B5-SQRTB5B5-4A5C52A5 =IFD5=E5, yes”,” no =IFB5B5=4A5C5, yes”,” no =-B6+SQRTB6B6-4A6C62A6 =-B6-SQRTB6B6-4A6C62A6 =IFD6=E6, yes”,” no =IFB6B6=4A6C6, yes”,” no =-B7+SQRTB7B7-4A7C72A7 =-B7-SQRTB7B7-4A7C72A7 =IFD7=E7, yes”,” no =IFB7B7=4A7C7, yes”,” no =-B8+SQRTB8B8-4A8C82A8 =-B8-SQRTB8B8-4A8C82A8 =IFD8=E8, yes”,” no =IFB8B8=4A8C8, yes”,” no =-B9+SQRTB9B9-4A9C92A9 =-B9-SQRTB9B9-4A9C92A9 =IFD9=E9, yes”,” no =IFB9B9=4A9C9, yes”,” no Table 2. the part of spreadsheet that is formatted with formulas. In the activity students are asked to enter different values of coefficient x 2 , coefficient of x, and the constant term and the formulas given will help them to get the corresponding values of first solution and second solution and then show whether the relation b 2 = 4ac is true or not. Students are supposed to continue entering different values of coefficient x 2 , coefficient of x, and the constant term, observing solutions and then check whether the relation b 2 = 4ac is true or not. Also students are instructed to draw graphs from the data they enter and calculate using the quadratic equations given, and then observe the nature of their graphs. After multiple attempts to the model the students may come to an understanding that for all perfect squares, they have repeated roots, the graphs cut the x-axis only once and the relation b 2 = 4ac is true, which is the general condition for a quadratic equation be a perfect square. 76 This activity facilitates the construction of an internal representation of the concept of perfect squares that may serve as the basis for learning the symbolic representation . This activity provides the translations between enactive, iconic, and symbolic representations that are necessary for learning abstract concepts. This allows the students to practice interpreting the graphs, tables and charts as they are presented and also helps to lighten the cognitive load and serve to organize each student’s understanding of a concept as the external representation embodies the concept to be learned.

5.4 What are the benefits for teachers and students